Abstract
We prove that, on connected compact manifolds, both C 1-generic conservative diffeomorphisms and C 1-generic transitive diffeomorphisms are topologically mixing. This is obtained through a description of the periods of a homoclinic class and by a control of the period of the periodic points given by the closing lemma.
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Dedicated to the 80th Anniversary of Professor Stephen Smale
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Abdenur, F., Crovisier, S. (2012). Transitivity and Topological Mixing for \({C}^{1}\) Diffeomorphisms. In: Pardalos, P., Rassias, T. (eds) Essays in Mathematics and its Applications. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28821-0_1
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DOI: https://doi.org/10.1007/978-3-642-28821-0_1
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